All clinical trials with a time-to-event endpoint are designed with reference to previous trials and/or data. Typically however, whilst historical information may guide issues such as sample size calculations or estimated event rates, this information is discarded when analysing the final results of a trial.
The exploration of more formal inclusion of historical information has gained at- tention. As far back as 1976, Pocock [190] was making a case for the use of historical controls in clinical trials. Importantly here, Pocock introduces six key criteria which
should be met in order to compare experimental treatments against historical controls. It has been noted by Speigelhalter et al. [21] that these conditions may be overly strin- gent and some relaxation may be reasonable, especially where some allocation is given to a control arm.
A further review by Sacks et al. [191] in 1982 compared the uses of randomised controlled trials to historical control trials and noted that using historical controls alone can lead to bias in the interpretation of trial results. Results such as this have lead to the domination of randomised control trials.
Attention has been given to the use of historical information to inform elements of a trial. Initially, the methodology was confined to carcinogenicity studies, Tarone [192] in particular introducing a method to incorporate historical information in a test for trends which has been used and adapted in practice [193, 194, 195]. With respect to trial design, Thall and Simon [196] consider the use of historical information for the formal use in the design of Phase II studies.
As an extension of the analyses for carcinogenicity trials, methodology for the incor- poration of historical information to the analysis of Poisson means has been developed [197, 198] with application of historical controls to the analysis of bioassay data ex- plored by Chen et al. [199]. Whilst methodology has being developed, its application outside of carcinogenicity trials remained sparse, despite reviews of Bayesian methods by Racine et al. [200] commenting on the ‘...tremendous scope for improved design and analysis using historical information’.
More recently, interest has grown with Ibrahim et al. [201] considering using his- torical information to adjust covariates in logistic regression models and French et al. considering their use in three-state models[202]. Chen et al. [203] consider the inclusion of historical controls into the the Bayesian design of non-inferiority trials with a binary endpoint.
One approach that has gained popularity is the use of power priors, see for example De Santis [204]. Here, it is assumed that some previous clinical trial data are available in their entirety. Historical and current data can then be analysed simultaneously with the results of the historical data informing the current data weighted by some power parameter. This approach was applied to survival data by Ibrahim et al. [58] and further by De Santi [183] who considers this approach for the use of Bayesian sample size calculations with a simple example set to the parametric exponential survival model.
Further to this, Neuenschwander et al. [205] introduce a meta-analytical approach of previous trial data for summarising the control information (MAP). Here a single parameter Îú is assumed to contain all information about a control arm in a trial. The meta analysis approach allows for both within and between study variability to be summarised and the authors suggest using the predictive distribution of Îú as a prior distribution for inclusion in the design and analysis of a future trial. Gsteiger et
al. [206] summarise Neuenschwander’s approach for the case of over dispersed Poisson data. Importantly here, aggregate data as well as complete data are used in estimating Îú.
The idea of a set of robust priors termed ‘commensurate’ has also been explored by Cook, [207] Fuquene et al. [208] and Hobbs et al.[209]. Here prior distributions influence the likelihood along with a ‘commensurability’ parameter which measures the degree of agreement between the information in the prior distributions and that collected in the data. Where the data agree with the prior information the priors are relatively informative; where there is poor agreement however, the posterior distributions are more dependent upon the observed data and the effect of the priors is lessened.
A recent review of the differing methods of incorporating historical information in the evaluation of a treatment effect is given by Viele et al. [210] comparing the [205] MAP method to the power prior approach, Pocock’s method and more rudimen- tary methods of pooling data. Though no recommendations are given, the authors do promote the methods as a means for obtaining smaller more efficient trials and for considering trials with allocation ratios other than the standard 1:1.
Whilst there is some well established methodology for the formal incorporation of historical priors into the analysis of clinical trials data, some key questions still remain unanswered. To date, much of of the methodology depends upon historical information being known in its entirety. This is often impractical. Furthermore, developing priors only on available data may introduce a level of selection bias into any analysis.
Whilst Gsteiger et al. [206] do explore the inclusion of aggregate data, the appli- cation of such an approach to survival data presents a number of challenges. Under a standard two arm trial, the control arm can be defined by the set of baseline hazard parameters and in the vast majority of survival models, sufficient information will not be reported for an aggregate meta analytical approach to be a viable option. Further- more, it is unlikely that a single parameter will be sufficient to contain all information regarding the control arm of a trial in this context.
In the remainder of this chapter, a method is proposed for estimating baseline hazard parameters where only summary information is available. Following the estimation of a historical baseline hazard function, some discussion is given to the definition of prior distributions and the effect these priors have on the design and analysis of a trial with a time-to-event endpoint.